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<p>Polarized cylinders in projective varieties have recently attracted considerable attention from the viewpoint of unipotent group actions on certain affine algebraic varieties. Let <i>S</i> be a del Pezzo surface with at worst Du Val singularities such that <i>S</i> admits an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((-K_S)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mo>-</mo> <msub> <mi>K</mi> <mi>S</mi> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-polar cylinder. A previous result by the author shows that there exists an <i>H</i>-polar cylinder for any ample <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {Q}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">Q</mi> </math></EquationSource> </InlineEquation>-divisor <i>H</i> on <i>S</i> when the degree of <i>S</i> is at least 3. In this article, we extend this result to the degree 2 case, by constructing an <i>H</i>-polar cylinder for any ample <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {Q}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">Q</mi> </math></EquationSource> </InlineEquation>-divisor on <i>S</i>.</p>

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Polarized Cylinders in Du Val del Pezzo Surfaces of Degree Two

  • 期刊论文

  • 发表日期：

    2026年6月23日

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  • Masatomo Sawahara

摘要

Polarized cylinders in projective varieties have recently attracted considerable attention from the viewpoint of unipotent group actions on certain affine algebraic varieties. Let S be a del Pezzo surface with at worst Du Val singularities such that S admits an \((-K_S)\) ( - K S ) -polar cylinder. A previous result by the author shows that there exists an H-polar cylinder for any ample \(\mathbb {Q}\) Q -divisor H on S when the degree of S is at least 3. In this article, we extend this result to the degree 2 case, by constructing an H-polar cylinder for any ample \(\mathbb {Q}\) Q -divisor on S.